n-Step Temporal Difference Learning with Optimal n

We consider the problem of finding the optimal value of n in the n-step temporal difference (TD) algorithm. We find the optimal n by resorting to the model-free optimization technique of simultaneous perturbation stochastic approximation (SPSA). We adopt a one-simulation SPSA procedure that is originally for continuous optimization to the discrete optimization framework but incorporates a cyclic perturbation sequence. We prove the convergence of our proposed algorithm, SDPSA, and show that it finds the optimal value of n in n-step TD. Through experiments, we show that the optimal value of n is achieved with SDPSA for any arbitrary initial value of the same.